Rate vs. timing (XVI) Flavors of spike-based theories (5) Rank order coding

I started with an overview of spike-based theories based on synchrony. I would like to stress that synchrony-based theories should not be mistaken for theories that predict widespread synchrony in neural networks. In fact, quite the opposite: as synchrony is considered as a meaningful event, it is implied that it is a rare event (since otherwise it would not be informative). But there are also theories that do not assign any particular role to synchrony, which I will discuss now.

One popular theory based on asynchrony is rank order coding or “first spike” theories. It was popularized in particular by Simon Thorpe, who showed that humans can categorize faces in such a small time that any neuron involved in the processing chain could fire little more than one spike. This observation discards theories based on temporal averages, both rate-based theories and interval-based theories. Instead, Simon Thorpe and colleagues proposed that the information is carried by the order in which spikes are fired. Indeed, receptors that are more excited (receiving more light) generally fire earlier, so that the order in which receptors are excited carries information that is isomorphic to the pattern of light on the retina. However, by itself, the speed of processing does not discard processing schemes that do not require temporal averages, for example synfire chains or rate-based schemes based on spatial averages. Indeed it is known that the speed at which the instantaneous firing rate of a population of noisy neurons can track a time-varying input is very fast and is not limited by the membrane time constant – an interesting point is that this fact is consistent with integrate-and-fire models and not with isopotential Hodgkin-Huxley models, but this is another story. However, one argument against rate-based schemes is that they are much less energetically efficient, since information is used only after averaging. To be more precise, a quantity can theoretically be estimated from the firing of N neurons with precision of order 1/N if their responses are coordinated, but of order 1/√N if the neurons are independent. In other words, the same level of precision requires N² neurons in a rate-based scheme, vs. N neurons in a spike-based scheme.

Computationally, first spike codes are not fundamentally different, at a conceptual level, from standard rate-based codes, because first spike latency is monotonically related to input intensity. However, one interesting difference is that if only the rank order, and not the exact timing, is taken into account, then this code becomes invariant to monotonous transformations of input intensity, for example global changes in contrast or luminance. However it is not invariant to more complex transformations.

Rank order codes are also different at a physiological level. Indeed an interesting aspect of this theory is that it acknowledges a physiological fact that is ignored by both rate-based theories and synchrony-based theories, namely the asymmetry between excitation and inhibition in neurons. How can a neuron be sensitive to the temporal order of its inputs? In synchrony-based theories, which rely on excitation, neurons are sensitive to the relative timing of their inputs rather than to their temporal order. Indeed temporal order is discontinuous with respect to relative timing: it abruptly switches at time lag 0. Such a discontinuity is provided by inhibition: excitation followed by inhibition is more likely to trigger a spike than inhibition followed by excitation. The asymmetry is due to the fact that spikes are produced when the potential exceeds a positive threshold (i.e., the trajectory crosses the threshold from below).

One criticism of rank order coding is that it requires a time reference. Indeed, when comparing two spike trains, any spike is both followed and preceded by a spike from the other train, unless only the “first spike” is considered. Such a time reference, which defines the notion of “first spike”, could be the occurrence of an ocular saccade, or the start of an oscillation period if there is a global oscillation in the network that can provide a common reference.

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